High-Resolution Spectroscopy from 3050 to 10000 A of the HDF-S QSO J2233-606 with UVES at the ESO VLT

We report on high-resolution observations ($\Re \simeq 45000$) of the Hubble Deep Field South QSO J2233-606 obtained with the VLT UV-Visual Echelle Spectrograph (UVES). We present spectral data for the wavelength region $3050 < \lambda < 10000$ \AA. The $S/N$ ratio of the final spectrum is about 50 per resolution element at 4000 \AA, 90 at 5000 \AA, 80 at 6000 \AA, 40 at 8000 \AA. Redshifts, column densities and Doppler widths of the absorption features have been determined with Voigt-profile fitting. A total of 621 lines have been measured. In particular 270 Ly-alpha lines, 41 Ly-beta and 24 systems containing metal lines have been identified. Together with other data in the literature, the present spectrum confirms that the evolution of the number density of Ly-alpha lines with $\log N($\huno$) > 14$ has an upturn at $z \sim 1.4-1.6$.Comment: 34 pages Latex, with 3 PostScript figures. Astronomical Journal, in press. A few revised upper limit

Is my ODE a Painleve equation in disguise?

Painleve equations belong to the class y'' + a_1 {y'}^3 + 3 a_2 {y'}^2 + 3 a_3 y' + a_4 = 0, where a_i=a_i(x,y). This class of equations is invariant under the general point transformation x=Phi(X,Y), y=Psi(X,Y) and it is therefore very difficult to find out whether two equations in this class are related. We describe R. Liouville's theory of invariants that can be used to construct invariant characteristic expressions (syzygies), and in particular present such a characterization for Painleve equations I-IV.Comment: 8 pages. Based on talks presented at NEEDS 2000, Gokova, Turkey, 29 June - 7 July, 2000, and at the AMS-HKMS joint meeting 13-16 December, 2000. Submitted to J. Nonlin. Math. Phy

Dependence of Dust Obscuration on Star Formation Rates in Galaxies

Many investigations of star formation rates (SFRs) in galaxies have explored details of dust obscuration, with a number of recent analyses suggesting that obscuration appears to increase in systems with high rates of star formation. To date these analyses have been primarily based on nearby (z < 0.03) or UV selected samples. Using 1.4 GHz imaging and optical spectroscopic data from the Phoenix Deep Survey, the SFR-dependent obscuration is explored. The use of a radio selected sample shows that previous studies exploring SFR-dependent obscurations have been biased against obscured galaxies. The observed relation between obscuration and SFR is found to be unsuitable to be used as an obscuration measure for individual galaxies. Nevertheless, it is shown to be successful as a first order correction for large samples of galaxies where no other measure of obscuration is available, out to intermediate redshifts (z ~ 0.8).Comment: 9 pages (including 5 encapsulated postscript figures), aastex, uses emulateapj5.sty. Accepted for publication in Ap

Studying the evolution of large-scale structure with the VIMOS-VLT Deep Survey

The VIMOS-VLT Deep Survey (VVDS) currently offers a unique combination of depth, angular size and number of measured galaxies among surveys of the distant Universe: ~ 11,000 spectra over 0.5 deg2 to I_{AB}=24 (VVDS-Deep), 35,000 spectra over ~ 7 deg2 to I_{AB}=22.5 (VVDS-Wide). The current ``First Epoch'' data from VVDS-Deep already allow investigations of galaxy clustering and its dependence on galaxy properties to be extended to redshifts ~1.2-1.5, in addition to measuring accurately evolution in the properties of galaxies up to z~4. This paper concentrates on the main results obtained so far on galaxy clustering. Overall, L* galaxies at z~ 1.5 show a correlation length r_0=3.6\pm 0.7. As a consequence, the linear galaxy bias at fixed luminosity rises over the same range from the value b~1 measured locally, to b=1.5 +/- 0.1. The interplay of galaxy and structure evolution in producing this observation is discussed in some detail. Galaxy clustering is found to depend on galaxy luminosity also at z~ 1, but luminous galaxies at this redshift show a significantly steeper small-scale correlation function than their z=0 counterparts. Finally, red galaxies remain more clustered than blue galaxies out to similar redshifts, with a nearly constant relative bias among the two classes, b_{rel}~1.4, despite the rather dramatic evolution of the color-density relation over the same redshift range.Comment: 14 pages. Extended, combined version of two invited review papers presented at: 1) XXVIth Astrophysics Moriond Meeting: "From Dark Halos to Light", March 2006, proc. edited by L.Tresse, S. Maurogordato and J. Tran Thanh Van (Editions Frontieres); 2) Vulcano Workshop 2006 "Frontier Objects in Astrophysics and Particle Physics", May 2006, proc. edited by F. Giovannelli & G. Mannocchi, Italian Physical Society (Editrice Compositori, Bologna

N-dimensional geometries and Einstein equations from systems of PDE's

The aim of the present work is twofold: first, we show how all the $n$-dimensional Riemannian and Lorentzian metrics can be constructed from a certain class of systems of second-order PDE's which are in duality to the Hamilton-Jacobi equation and second we impose the Einstein equations to these PDE's

A contribution to the selection of emission-line galaxies using narrow-band filters in the optical airglow windows

Emission line galaxies are an invaluable tool for our understanding of the evolution of galaxies in the Universe. Imaging of deep fields with narrow-band filters allows not only the selection of these objects, but also to infer the line flux and the equivalent width of the emission line with some assumptions. The narrow-band filter technique provides homogeneous samples of galaxies in small comoving volumes in the sky. We present an analysis of the selection of emission-line galaxies using narrow-band filters. Different methods of observation are considered: broad-band -- narrow-band filters and two broad-band and one narrow-band filters. We study also the effect of several lines entering simultaneously inside the filters (this is the case of Halpha). In each case the equations to obtain the equivalent width and line flux from the photometry are obtained. Candidates to emission-line objects are selected by their color excess in a magnitude-color diagram. For different narrow-band filters, we compute the mean colors of stars and galaxies, showing that, apart from galaxies, some types of stars could be selected with certain filter sets. We show how to compute the standard deviation of the colors of the objects even in the usual case when there are not enough objects to determine the standard deviation from the data. We present also helpful equations to compute the narrow-band and the broad-band exposure times in order to obtain minimum dispersion in the ratio of fluxes of both bands with minimum total exposure time.Comment: Accepted for publication in PASP 48 pages, 10 figures Corrected typos, fixed references. Updated reference to T

Star formation rate indicators in the Sloan Digital Sky Survey

The Sloan Digital Sky Survey (SDSS) first data release provides a database of 106000 unique galaxies in the main galaxy sample with measured spectra. A sample of star-forming (SF) galaxies are identified from among the 3079 of these having 1.4 GHz luminosities from FIRST, by using optical spectral diagnostics. Using 1.4 GHz luminosities as a reference star formation rate (SFR) estimator insensitive to obscuration effects, the SFRs derived from the measured SDSS Halpha, [OII] and u-band luminosities, as well as far-infrared luminosities from IRAS, are compared. It is established that straightforward corrections for obscuration and aperture effects reliably bring the SDSS emission line and photometric SFR estimates into agreement with those at 1.4 GHz, although considerable scatter (~60%) remains in the relations. It thus appears feasible to perform detailed investigations of star formation for large and varied samples of SF galaxies through the available spectroscopic and photometric measurements from the SDSS. We provide herein exact prescriptions for determining the SFR for SDSS galaxies. The expected strong correlation between [OII] and Halpha line fluxes for SF galaxies is seen, but with a median line flux ratio F_[OII]/F_Halpha=0.23, about a factor of two smaller than that found in the sample of Kennicutt (1992). This correlation, used in deriving the [OII] SFRs, is consistent with the luminosity-dependent relation found by Jansen et al. (2001). The median obscuration for the SDSS SF systems is found to be A_Halpha=1.2 mag, while for the radio detected sample the median obscuration is notably higher, 1.6 mag, and with a broader distribution.Comment: Accepted for publication in ApJ, 40 pages, 26 figure

HeII emitters in the VIMOS VLT Deep Survey: PopIII star formation or peculiar stellar populations in galaxies at 2<z<4.6?

The aim of this work is to identify HeII emitters at 2<z<4.6 and to constrain the source of the hard ionizing continuum that powers the HeII emission. We have assembled a sample of 277 galaxies with a high quality spectroscopic redshift at 2<z<4.6 from the VVDS survey, and we have identified 39 HeII1640A emitters. We study their spectral properties, measuring the fluxes, equivalent widths (EW) and FWHM for most relevant lines. About 10% of galaxies at z~3 show HeII in emission, with rest frame equivalent widths EW0~1-7A, equally distributed between galaxies with Lya in emission or in absorption. We find 11 high-quality HeII emitters with unresolved HeII line (FWHM_0<1200km/s), 13 high-quality emitters with broad He II emission (FWHM_0>1200km/s), 3 AGN, and an additional 12 possible HeII emitters. The properties of the individual broad emitters are in agreement with expectations from a W-R model. On the contrary, the properties of the narrow emitters are not compatible with such model, neither with predictions of gravitational cooling radiation produced by gas accretion. Rather, we find that the EW of the narrow HeII line emitters are in agreement with expectations for a PopIII star formation, if the episode of star formation is continuous, and we calculate that a PopIII SFR of 0.1-10 Mo yr-1 only is enough to sustain the observed HeII flux. We conclude that narrow HeII emitters are either powered by the ionizing flux from a stellar population rare at z~0 but much more common at z~3, or by PopIII star formation. As proposed by Tornatore et al. (2007), incomplete ISM mixing may leave some small pockets of pristine gas at the periphery of galaxies from which PopIII may form, even down to z~2 or lower. If this interpretation is correct, we measure at z~3 a SFRD in PopIII stars of 10^6Mo yr^-1 Mpc^-3 qualitatively comparable to the value predicted by Tornatore et al. (2007).Comment: accepted for publication in A&

The Star Formation Rate Density and Dust Attenuation Evolution over 12 Gyr with the VVDS Surveys

[Abridged] We investigate the global galaxy evolution over 12 Gyr (0.05<z<4.5), from the star formation rate density (SFRD), combining the VVDS Deep (17.5<=I<=24.0) and Ultra-Deep (23.00<=i<=24.75) surveys. We obtain a single homogeneous spectroscopic redshift sample, totalizing about 11000 galaxies. We estimate the rest-frame FUV luminosity function (LF) and luminosity density (LD), extract the dust attenuation of the FUV radiation using SED fitting, and derive the dust-corrected SFRD. We find a constant and flat faint-end slope alpha in the FUV LF at z1.7, we set alpha steepening with (1+z). The absolute magnitude M*_FUV brightens in the entire range 02 it is on average brighter than in the literature, while phi* is smaller. Our total LD shows a peak at z=2, present also when considering all sources of uncertainty. The SFRD history peaks as well at z=2. It rises by a factor of 6 during 2 Gyr (from z=4.5 to z=2), and then decreases by a factor of 12 during 10 Gyr down to z=0.05. This peak is mainly produced by a similar peak within the population of galaxies with -21.5<=M_FUV<=-19.5 mag. As times goes by, the total SFRD is dominated by fainter and fainter galaxies. The presence of a clear peak at z=2 and a fast rise at z>2 of the SFRD is compelling for models of galaxy formation. The mean dust attenuation A_FUV of the global galaxy population rises by 1 mag during 2 Gyr from z=4.5 to z=2, reaches its maximum at z=1 (A_FUV=2.2 mag), and then decreases by 1.1 mag during 7 Gyr down to z=0. The dust attenuation maximum is reached 2 Gyr after the SFRD peak, implying a contribution from the intermediate-mass stars to the dust production at z<2.Comment: 23 pages, 15 figures, accepted for publication in A&

Invariants of pseudogroup actions: Homological methods and Finiteness theorem

We study the equivalence problem of submanifolds with respect to a transitive pseudogroup action. The corresponding differential invariants are determined via formal theory and lead to the notions of k-variants and k-covariants, even in the case of non-integrable pseudogroup. Their calculation is based on the cohomological machinery: We introduce a complex for covariants, define their cohomology and prove the finiteness theorem. This implies the well-known Lie-Tresse theorem about differential invariants. We also generalize this theorem to the case of pseudogroup action on differential equations.Comment: v2: some remarks and references addee